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arXiv · 2503.14635

Non-Degenerate Multilinear Singular Multipliers with Fractional Rank

Jianghao Zhang
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Abstract

We establish $L^p$ estimates for multilinear multipliers acting on $(n-1)$-tuples of functions on $\mathbb{R}^d$. We assume that the multiplier satisfies symbol estimates outside a linear subspace of dimension $m$. The difficulty of proving $L^p$ bounds increases with the rank $\frac{m}{d}$, and our focus is on the fractional rank case $\frac{m}{d}<\frac{n}{2}\leq \lceil \frac{m}{d}\rceil$.

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Jianghao Zhang. 2025-03-18. Non-Degenerate Multilinear Singular Multipliers with Fractional Rank. https://arxiv.org/abs/2503.14635

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